Low-rank optimization is a ubiquitous and powerful technique at the heart of unsupervised machine learning, and it continues to be a flourishing field of research with a broad spectrum of practical applications. However, modern data present unique challenges for signal processing algorithms. Such data often contain noise, missing entries, gross outliers, or system dynamics, and are also increasingly high-dimensional or even multi-way, increasing the storage and computational burden. In this talk, I will discuss several fast and computationally efficient low-rank matrix and tensor factorization algorithms adept at recovering large-scale data from incomplete, noisy, and/or streaming observations. Specifically, I will introduce our recent work in online Grassmannian optimization algorithms and probabilistic principal component analysis algorithms for heterogeneous data. I will show success of our methods on panoramic video separation, under-sampled MRI data, and data with heteroscedastic noise. Speaker(s): Kyle Gilman (University of Michigan)